Simplify; express your answer in exponential form. Assume $x\neq 0, y\neq 0$. $\dfrac{{x^{4}y^{-2}}}{{(x^{3}y^{2})^{-5}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${x^{4}y^{-2} = x^{4}y^{-2}}$ On the left, we have ${x^{4}}$ to the exponent ${1}$ . Now ${4 \times 1 = 4}$ , so ${x^{4} = x^{4}}$ Apply the ideas above to simplify the equation. $\dfrac{{x^{4}y^{-2}}}{{(x^{3}y^{2})^{-5}}} = \dfrac{{x^{4}y^{-2}}}{{x^{-15}y^{-10}}}$ Break up the equation by variable and simplify. $\dfrac{{x^{4}y^{-2}}}{{x^{-15}y^{-10}}} = \dfrac{{x^{4}}}{{x^{-15}}} \cdot \dfrac{{y^{-2}}}{{y^{-10}}} = x^{{4} - {(-15)}} \cdot y^{{-2} - {(-10)}} = x^{19}y^{8}$